def backward_propagation_L2(X, Y, cache, lambd):
'''
反向传播,只在计算dW时发生了变化，其他地方不变
'''
(A1, Z1, W1, b1, A2, Z2, W2, b2, A3, Z3, W3, b3) = cache
m = Y.shape[1] # 样本个数
dA3 = -(np.divide(Y, A3) - np.divide(1 - Y, 1 - A3))
dZ3 = AF.sigimoid_backward(dA3, Z3)
dW3 = 1. / m * np.dot(dZ3, A2.T) + (lambd * W3 / m)
db3 = 1. / m * np.sum(dZ3, axis=1, keepdims=True)
dA2 = np.dot(W3.T, dZ3)
dZ2 = AF.relu_backward(dA2, Z2)
dW2 = 1. / m * np.dot(dZ2, A1.T) + (lambd * W2 / m)
db2 = 1. / m * np.sum(dZ2, axis=1, keepdims=True)
dA1 = np.dot(W2.T, dZ2)
dZ1 = AF.relu_backward(dA1, Z1)
dW1 = 1. / m * np.dot(dZ1, X.T) + (lambd * W1 / m)
db1 = 1. / m * np.sum(dZ1, axis=1, keepdims=True)
grads = {
'dW1': dW1,
'dW2': dW2,
'dW3': dW3,
'db1': db1,
'db2': db2,
'db3': db3
}
return grads
def linear_activation_backward(dA, cache, activation):
"""
Implement the backward propagation for the LINEAR->ACTIVATION layer.
Arguments:
dA -- post-activation gradient for current layer l
cache -- tuple of values (linear_cache, activation_cache) we store for computing backward propagation efficiently
activation -- the activation to be used in this layer, stored as a text string: "sigmoid" or "relu"
Returns:
dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev
dW -- Gradient of the cost with respect to W (current layer l), same shape as W
db -- Gradient of the cost with respect to b (current layer l), same shape as b
"""
linear_cache, activation_cache = cache
if (activation == 'sigmoid'):
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
elif (activation == 'relu'):
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
return dA_prev, dW, db
def backward_propagation_dropout(X, Y, cache, keep_prob):
'''
加入dropout的反向传播
'''
(A1, D1, Z1, W1, b1, A2, D2, Z2, W2, b2, A3, Z3, W3, b3) = cache
m = Y.shape[1] # 样本个数
dA3 = -(np.divide(Y, A3) - np.divide(1 - Y, 1 - A3))
dZ3 = AF.sigimoid_backward(dA3, Z3)
dW3 = 1. / m * np.dot(dZ3, A2.T)
db3 = 1. / m * np.sum(dZ3, axis=1, keepdims=True)
dA2 = np.dot(W3.T, dZ3)
dA2 = dA2 * D2 # step1 使用正向传播时未关闭的节点
dA2 = dA2 / keep_prob # step2 缩放未舍弃节点的值
dZ2 = AF.relu_backward(dA2, Z2)
dW2 = 1. / m * np.dot(dZ2, A1.T)
db2 = 1. / m * np.sum(dZ2, axis=1, keepdims=True)
dA1 = np.dot(W2.T, dZ2)
dA1 = dA1 * D1 # step1 使用正向传播时未关闭的节点
dA1 = dA1 / keep_prob # step2 缩放未舍弃节点的值
dZ1 = AF.relu_backward(dA1, Z1)
dW1 = 1. / m * np.dot(dZ1, X.T)
db1 = 1. / m * np.sum(dZ1, axis=1, keepdims=True)
grads = {
'dW1': dW1,
'dW2': dW2,
'dW3': dW3,
'db1': db1,
'db2': db2,
'db3': db3
}
return grads
